INVARIANT-MEASURES FOR A 2-SPECIES ASYMMETRIC PROCESS

We consider a process of two classes of particles jumping on a one-dimensional lattice. The marginal system of the first class of particles is the one-dimensional totally asymmetric simple exclusion process. When classes are disregarded the process is also the totally asymmetric simple exclusion process. The existence of a unique invariant measure with product marginals with density rho and lambda for the first- and first- plus second-class particles, respectively, was shown by Ferrari, Kipnis, and Saada. Recently Derrida, Janowsky, Lebowitz, and Speer have computed this invariant measure for finite boxes and performed the infinite-volume limit. Based on this computation we give a complete description of the measure and derive some of its properties. In particular we show that the invariant measure for the simple exclusion process as seen from a second-class particle with asymptotic densities rho and lambda is equivalent to the product measure with densities rho to the left of the origin and lambda to the right origin.